ASYMPTOTIC-EXPANSION OF SHIP CAPSIZING IN RANDOM SEA WAVES .2. 2ND-ORDER APPROXIMATION

This is a continuation of Part I [lnt. J. Non-Linear Mech. 30, 727-740 (1995)] on the first-passage problem of ship roll oscillations in a r andom sea. A new coordinate system based on the canonical action-angle variables is used to express ship roll motion in terms of a set of It o stochastic differential equations. The Pontryagin equation which des cribes the mean exit time of the system is solved using the method of asymptotic expansion. In the present analysis, a second-order approxim ation is carried out. The solution includes the contribution of the bo undary layer, which compensates for the residual in the boundary condi tion at the barrier. It is found that the second-order approximation s olution yields better results and takes into account such effects as t he mean value of the excitation and other additional non-linearities w hich were not accounted for in the first-order approximation.